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3.3. Compound Systems

In the following s = v, z or s depending on whether we have a Fourier transform, Z-transform or a Laplace transform.

A. Cascade systems

H(s) = Y(s) = Y(s) · Y1(s) = H1(s) H2(s)
X(s) Y1(s) X(s)

B. Parallel systems

H(s) = Y(s) = Y1(s) + Y2(s) = Y1(s) + Y2(s) = H1(s) + H2(s)
X(s) X(s) X(s) X(s)

C. Feedback systems

X1(s) = X(s) + Y1(s)
Y1(s) = H2(s) Y(s)
Y(s) = H1(s) X1(s)
H(s) = Y(s) = H1(s) X1(s) = H1(s) X(s) + H1(s) Y1(s)
X(s) X(s) X(s)
        = H1(s) + H1(s) H2(s) Y(s) = H1(s) + H1(s) H2(s) H(s)
X(s)
=>         H(s) = H1(s)
1 - H1(s) H2(s)

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